History and Philosophy of Science

Neither meaning nor truth (nor practical value) in formal mathematics

At my IIT (BHU) lecture (see also previous post), I emphasized Bertrand Russell’s remark that there is neither meaning nor truth in (formal) mathematics. Hence, any nonsense proposition one desires (such as “All rabbits have two horns”) can be proved as a formal mathematical theorem from appropriate postulates: Russell’s sole criterion being that the postulates should be “amusing”.

To drive the point home, I pointed out how, long ago, when I still believed in formal math, I used to teach a course (A) on Real Analysis while also teaching a more advanced course (B) on Advanced Functional Analysis, in the math department of Pune University. In the elementary course (A) I taught

Theorem: A differentiable function must be continuous. (Therefore, a discontinuous function cannot be differentiated.).

In the more advanced course (B) I taught

Theorem: Any (Lebesgue) integrable function can be differentiated infinitely often. (Therefore, a function with simple discontinuities can be differentiated infinitely often.)

I have made exactly this point earlier in this blog.

“Now, for several years I taught real analysis to students and mathematically proved in class that a discontinuous function cannot be differentiated. I also taught advanced functional analysis (and topological vector spaces and the Schwartz theory according to which every Lebesgue integrable function can be differentiated). In the advanced class, I mathematically proved the exact opposite that a function with a simple discontinuity can be differentiated infinitely often (and the first derivative is the Dirac δ).”

The question is which definition of the derivative should one use for the differential equations of physics? As pointed out in Cultural Foundations of Mathematics (or see this paper) the issue can only be decided empirically, unless the aim, like that of Stephen Hawking and G. F. R. Ellis, is to spread Christian superstitions about creation using bad mathematics.

Superstitions go naturally with ignorance. One such ignorant professor from the IIT mathematics department was present during my lecture. His knowledge was limited to the first of the theorems above, and he ignorantly believed that it was some kind of absolute truth, which everyone was obliged to believe. He objected to my claim that a discontinuous function can, of course, be differentiated, and walked out to show his contempt of my claim.

Even the students had heard of the Dirac δ, and agreed with me. The next day during the workshop, I explained that I had engaged with this question since my PhD thesis. But the professor remained absent, though his ignorance was exposed before the students. He is welcome to respond by email; I will post it publicly since it is sure to further expose his ignorance.

Oliver Heaviside applied first applied this to problems of electrical engineering over a century ago, and Dirac, formerly an electrical engineer, then applied the Dirac δ to physics. It remains very useful because it is the Fourier transform of white noise (flat spectrum or the unit function), and used even in the formal mathematical theory of Brownian motion.

Earlier in the lecture, the same professor, contested my claim that probability was invented in ancient India, and taken from India in the 16th c., where credit for it was later falsely given to people like Pascal and Poisson. (more…)

By C. K. Raju, ago

Decolonising humanities in Beirut

A conference on decolonisation of humanities was organized at Al Maaref University, Beirut.
General view of the conference
The big concern was how colonial education has altered human values. But Western education did not come for humanities, therefore my point was that merely changing humanities education won’t result in the desired change.  The facts are (1) Western education came to the colonised as church education. (2) It was and is justified  on the grounds that the colonised need science. The net effect of (2) is that the colonised foolishly trust the authority of church institutions like Cambridge, Oxford, and Paris. This way the church is able to mix all sorts of subtle poison in university education, even through math and science.
CKR at Beirut conference
Though Western education ostensibly came for science it ensures that the mass of educated are ignorant of math and science, so they are forced to trust authority (of the West, obviously). It further anti-educates them by planting myths, and teaching them to think in terms of stories. For example, due to such indoctrination, the colonised are trapped in the myth that science and church are at war. They failed to notice the obvious fact, contrary to this myth, that colonial education came as 100% church education, and that, for example, the best science colleges, even in India, are still church institutions.
Mind control of the colonised was the work of the church, in  collusion with the colonial state. This persists, like Western education, even after direct political control of the colonised ended. Once the colonised are rendered ignorant, and taught to trust Western authority and myths, as Western education teaches, there is no solution for them.
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By C. K. Raju, ago

The racist nitwits of Cape Town

A reporter from Africa met me recently in India to find out about the events concerning the panel discussion on decolonisation in Cape Town, a year ago. Someone here asked: could he be a church agent, who may again present a biased picture? I don’t know. But he does not seem to know any math, and may not have understood my critique of formal math. So, to make sure that others (especially the ill-informed) do not “control the narrative”, and totally misrepresent it, it is time I put up my side of things.
An important background, to the debate last year in the University of Cape Town, which has not been adequately mentioned, is my book The Eleven Pictures of  Time (Sage 2003). In it I extensively criticised the book Large Scale Structure of Space-Time by Stephen Hawking, and G. F. R. Ellis, of the University of Cape Town. (Note, in passing, that Hawking unethically collaborated with Ellis at a time when there was an academic boycott of apartheid.) My key issue with the Hawking and Ellis book was that their conclusions about a “singularity” involved bad mathematics, and a bad understanding of calculus (even from within  formal mathematics).
But let us go one step at a time. First, their conclusion that the cosmos began with a  “singularity” was not science (since not refutable on Popper’s criterion). Second, their conclusion was of great political significance to the church, through the claim that science supports the church’s religious dogmas of creation. The  mathematical conclusion of a singularity is explicitly connected by Hawking and  Ellis to religious beliefs about creation and other dogmas. The key takeaway of their book (p. 364) is that “the actual point of creation, the singularity, is outside  the presently known laws of physics.”
The belief that God rules the world with eternal “laws” of nature is itself a religious church dogma first articulated by Aquinas, not a scientific (refutable) belief. Simply put, the church supports it, but Hinduism, Buddhism and Islam deny it.  (See this minuted discussion for example, which explains that Hinduism accepts rta, but not immutable laws, for Buddhism, see the video “Buddhism and science”, for Islam see the keynote and article on Islam and science.) Further, other religions accept continuous creation, or the creativity of living organisms (not continuous creation in the mechanistic sense of the theory of Bondi, Gold, Hoyle and Narlikar). The big bang theory alone is NOT the opposite of continuous creation. The “singularity”, interpreted as a beginning of time, relates to creation  more clearly than the big bang, which need not be a true beginning of time, but could be just the other side of a big crunch in an oscillating cosmos.
There is no doubt about the religiosity of the book by Hawking and Ellis. Ellis got  the million dollar Templeton award, for putting together science and religion, and Hawking never got the Nobel prize! The church greatly glorified Stephen Hawking, and that church propagandist support helped sell millions of copies of his book  Brief History of Time which restated the conclusions of singularity theory for a lay audience.  But singularities and creationism are simply not physics. Therefore, much as Hawking desired the Nobel prize, and much as the Nobel prize committee may have wanted to give it to him, they simply could not do so.
The physicist F. J. Tipler (Physics of Immortality) pushed this connection of science and religion via singularity theory. He explicitly claimed that singularity theory proves the truth of Judeo-Christian theology. In the opening paragraphs, Tipler said his book aimed

“to show that the central claims of Judeo-Christian theology are in fact true, that these claims are straightforward deductions of the laws of physics as we now understand them. I have been forced into these conclusions by the inexorable logic of my own special branch of physics…the area of global general relativity…created…by the great British physicists Roger Penrose and Stephen Hawking.”

The colonised mind may talk against creationism, in support of Darwinism, but it never dared contest this kind of religious claim of creationism backed by Western authority. Despite the millions who read Stephen Hawking’s book, Brief History of Time, I have not heard a SINGLE other dissenting voice in the last thirty years. (more…)

By C. K. Raju, ago

Israel denies visa for talk on decolonisation exposing Einstein

The Palestine Technical University, Kadourie, Palestine, is organizing the Sixth Palestinian Conference on Modern Trends in Mathematics and Physics PCMTMP-VI, 5th-8th August 2018.
I was invited to give two plenary talks (scheduled on 7th and 8th Aug) on
Decolonising mathematics: how and why it makes science better (and enables students to solve harder problems)
An extended summary and abstract of my proposed talk are posted online.
The Israeli embassy has, however, refused me a visa. No official reason or explanation was offered for the denial of visa. When I asked, an official from the Israeli embassy did very rudely warn me not to apply ever again for an Israeli visa.
Now five years ago, I visited Palestine (See blog post “Mathematics in refugee camps”, and a nice video on History and Philosophy of science). Of course, I did have a terrible experience with the Israelis: they charged me some USD 200 for a taxi for 8.5 km, then put me on a share taxi and promised to give the receipt after I crossed the border! Never encountered such terrible cheats anywhere else in the world. But last time the Israeli embassy in India had issued me a visa.
So, I am left wondering what has changed. Three things have changed. 1. Decolonisation, 2. Einstein, and 3. Indo-Israeli relationship
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By C. K. Raju, ago

Alternative math: media reports

Here are the media reports for the Rajju Ganit workshop from Dainik Bhaskar, Nai Duniya, Talk show by Global Herald, and Free Press Journal Global Herald talk show प्रसिद्ध गणितज्ञ सीके राजू से खास चर्चा Dainik Bhaskar Nai Duniya26 June 2018 Global Herald e-paper 30 June 2018 Free Press journal

By C. K. Raju, ago

George Joseph: serial plagiarist

1-The fraud-news blitz

Ten years ago, on 14/15 Aug 2007, on the 60th anniversary of India’s independence, PTI London released a piece of fraud news. All major newspapers in India prominently carried it, Hindustan Times on the front page, The Hindu on the back page etc. According to the news, two British researchers from Manchester and Exeter universities had established that the calculus developed in India before Newton. But they added that this left Newton’s greatness unaffected.
The news was based on a press release posted on the Manchester university website (now removed from its site, since it was a fraud, but archived here).
The news was also carried internationally, for example, by the London Telegraph. I phoned them, and pointed out that I had recently published a whole book dealing with the transmission of the calculus. Cultural Foundations of Mathematics (Pearson Longman. 2007). The subtitle of the book itself said this: it was “The nature of mathematical proof, and the transmission of the calculus from India to Europe in the 16th c. CE”. The book emphasized the development of calculus in India with a different philosophy of mathematics, and its theft by Cochin-based Jesuits. This theft of knowledge was carried out to solve the major scientific challenge then facing Europe: navigation. But, after stealing it, the same churchmen wrote utterly false histories glorifying the West by claiming that Newton and Leibniz invented the calculus. Colonialism was built on this false history, not any technological superiority, as I have explained elsewhere.
My calculus book was the culmination of a ten year effort since 1997, partly funded by two agencies: the Indian National Science Academy since 1998 (Project on Madhava and the Origin of the Calculus), and the Project of History of Indian Science, Philosophy and Culture, with which I was associated since its inception in the early 90’s, but accepted an Editorial Fellowship only in 1999. The 500-page book (an authored volume, not an edited volume) was the 50th volume in the PHISPC series.
When I brought this to the notice of the London Telegraph they said they had not checked the news, and removed the fraud news item from their website.
In Hindustan Times the front page news carried the signature of Vijay Dutt their London correspondent.
HT front page news
I contacted the HT office, and further pointed out that one of the purported authors of the Manchester paper had been earlier involved in plagiarising my work and warned in 2004 by Exeter University. The HT had given prominent coverage to that news in 2004.HT plagiarism report 8 Nov 2004
(If the above is difficult to read, download the pdf file posted here.) (more…)

By C. K. Raju, ago

Infinity, math, physics, and metaphysics

Can physics be done without infinity as taught in math (real analysis) today? Someone demanded an explanation in an email sent to my son.  (I guess the Raju family has the same problem as the Bernoulli family in Europe!  🙂 .)
Ordinarily, I would not have responded, for people ought not to demand an explanation by email without bothering to read or understand what I have already written. But, similar doubts were expressed by a young woman (with a PhD in functional analysis) who attended my talk in Ramallah. They may again arise in future. So, I decided to respond.
Infinity is metaphysics. Infinity relates to eternity, so that the Western concept of infinity in present-day math is saturated with the church metaphysics of eternity.
Ironically, the figure for infinity, ∞, is still shaped like a serpent coiled back on itself and eating its own tail, and is an old symbol of quasi-cyclic time.
The linkage of infinity to eternity led to the first creationist controversy: over the nature of eternity, not evolution. In the 6th c. John Philoponus objected to Proclus’ notion of eternity based on quasi-cyclic time. Philoponus’ problem was that if the cosmos is eternal (as Proclus conceived it) it would not be created. That creationist controversy is still going on.
For example, Stephen Hawking claimed the cosmos was created with a “singularity”. (A “singularity” is nothing but an infinity of some sort.)  He concluded his only serious scientific book by identifying the “singularity” with “the actual point of creation” where there is a breakdown of the “laws of physics”. This conclusion is pure metaphysics, for there is no way to check it empirically.
In his popular book, Hawking explained the point of this metaphysical conclusion: because the “laws of physics” break down at the “singularity”, that leaves God free to create the world of his choice. Note that this is in accordance with the Christian notion of one-time creation (and contrary to the Islamic notion of continuous creation, or the Buddhist notion of non-creation, or the “Hindu” notion of periodic creation and destruction). The church heavily promoted this “scientific proof” of the correctness of its (post-Nicene) Christian theology.
People may be suspicious of the church but they implicitly trust scientists today. And, though few  (perhaps 2 or 3 among the 1.25 billion in India) have read or understood Hawking’s scientific work, hundreds of millions of people strongly believe he is a great scientist. Such gullibility and implicit trust is bound to be exploited by the church, which is ever on the lookout for new ways of doing its propaganda. Few people are even aware that Hawking reached his conclusion by postulating his “chronology condition” which denies quasi-cyclic time, and does so using exactly the same bad argument that Augustine used against Origen,  and which argument is at the foundation of post-Nicene Christianity. So, what Hawking did was to use the metaphysics of infinity to promote the politics of the church, like Augustine.
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By C. K. Raju, ago